60. A dog trainer is exploring the relationship between the size of the dog (weight in kilometres [km]) and its daily food consumption (measured in cups). Below is the result of a sample of 18 observations: Km Cups Km Cups Km Cups 41 3 37 3 49 3 148 8 111 6 113 6 79 5 41 3 84 5 41 4 91 5 95 5 85 5 109 6 57 4 111 6 207 10 168 9

a. Compute the correlation coefficient. Is it reasonable to conclude that the correlation in the population is greater than zero? Use the 0.05 significance level.

b. Develop the regression equation for cups on the basis of the dog’s weight. How much does each additional cup change the estimated weight of the dog?

f to study the relationship between the amount of fire damage and the distance between the burning house and the nearest fire station. This information will be used in setting rates for insurance coverage. For a sample of 30 claims for the last year, the director of the actuarial department determined the distance from the fire station (X) and the amount of fire damage, in thousands of dollars (Y). The computer output is as follows: ANOVA table Source SS df MS F Regression 1,864.5782 1 1,864.5782 38.83 Residual 1,344.4934 28 48.0176 Total 3,209.0716 29 Regression output Variables Coefficients Std. Error t(df = 28) Intercept 12.3601 3.2915 3.755 Distance–X 4.7956 0.7696 6.231

a. Write out the regression equation. Is there a direct or indirect relationship between the distance from the fire station and the amount of fire damage?

b. How much damage would you estimate for a fire 5 km from the nearest fire station?

c. Determine and interpret the coefficient of determination.

d. Determine the correlation coefficient. Interpret its value. How did you determine the sign of the correlation coefficient?

e. Conduct a test of hypothesis to determine if there is a significant relationship between the distance from the fire station and the amount of damage. Use the 0.01 significance level and a two-tailed test.